The problem of fault diagnosis has been discussed widely, and the diagnosability of many well-known networks has been explored. Strong diagnosability, and conditional diagnosability are both novel measurements for evaluating reliability and fault tolerance of a system. In this paper, some useful sufficient conditions are proposed to determine strong diagnosability, and the conditional diagnosability of a system. We then apply them to show that an n-dimensional augmented cube AQ n is strongly (2n-1)-diagnosable for n ≥ 5, and the conditional diagnosability of AQ n is 6n-17 for n ≥ 6. Our result demonstrates that the conditional diagnosability of AQ n is about three times larger than the classical diagnosability.
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